Complex Variable Function Solution Of Elasticity For Stress Of Surrounding Rock And Depth Of Bottom Failure In Stope

Accurately obtaining the stress distribution of the surrounding rock of the stope and the depth of the floor can provide the necessary basic data for the prevention and control of coal mining water damage above the confined water,and have important theoretical significance and technical guidance for coal mine safety production.Elastic mechanics complex variable function method has a unique advantage in solving the problem of orifice.Many scholars have also applied it to the stress solution of circular roadway,but the results of systematic research on stress distribution of surrounding rock in stope(rectangular section)by this method are less.This paper uses the method of elastic mechanics complex variable function to study the stress distribution of the surrounding rock around the different propulsion distance and different rock dip angles.On this basis,the damage depth of the floor is calculated and its failure characteristics are analyzed.The main results of the study are as follows.1)Comparing the three-dimensional numerical model with the two-dimensional plane stress model,it is concluded that when the excavation distance is less than or equal to 0.3 times of the excavation width,the error between the plane model and the three-dimensional model is small,and the plane model can be approximated to solve the surrounding rock stress.However,regardless of the ratio of excavation length to width,the error between the three-dimensional model and the plane stress model is small in the middle of excavation.2)The accuracy of mapping function decreases gradually with the increase of the advancing length,which results in the decrease of the accuracy of analytical solution obtained by complex variable function method.To ensure the accuracy of calculation,the maximum acceptable length-to-height ratio is 6:1.the horizontal stress,vertical stress and deviating stress in both sides of goaf concentrate,and the stress in roof and floor area diffuses.and the stress set increases with the advancing distance.The failure mode of the floor is symmetrical,and the depth increases gradually with the increase of the propulsion distance.However,when the propulsion distance increases to 25 m,the failure depth of the floor will not increase,and will stabilize at about 18 m.3)With the increase of inclination angle,the accuracy of stress component expression decreases gradually,resulting in the error of analytical solution obtained by complex variable function method increasing gradually.When inclination angle increases from10 degrees to 30 degrees,the error increases from 2.93% to 9.50%.The stress concentration degree at the end of goaf is greater than that at the level of stope,while the stress diffusion degree of roof and floor is less than that at the level of stope.The maximum failure depth of the floor moves downward from the middle of the working face,and along the inclined direction of the coal seam,the failure depth of the lower side of the working face is greater than that of the upper side.the whole floor of the working face in the inclined direction of the rock seam presents a "spoon" failure pattern of large and small bottom.Figure [49] Table [8] reference [100]...